zspr (l) - Linux Manuals

zspr: performs the symmetric rank 1 operation A := alpha*x*conjg( xaq ) + A,

NAME

ZSPR - performs the symmetric rank 1 operation A := alpha*x*conjg( xaq ) + A,

SYNOPSIS

SUBROUTINE ZSPR(
UPLO, N, ALPHA, X, INCX, AP )

    
CHARACTER UPLO

    
INTEGER INCX, N

    
COMPLEX*16 ALPHA

    
COMPLEX*16 AP( * ), X( * )

PURPOSE

ZSPR performs the symmetric rank 1 operation where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form.

ARGUMENTS

UPLO (input) CHARACTER*1
On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = aqUaq or aquaq The upper triangular part of A is supplied in AP. UPLO = aqLaq or aqlaq The lower triangular part of A is supplied in AP. Unchanged on exit.
N (input) INTEGER
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA (input) COMPLEX*16
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X (input) COMPLEX*16 array, dimension at least
( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N- element vector x. Unchanged on exit.
INCX (input) INTEGER
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
AP (input/output) COMPLEX*16 array, dimension at least
( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = aqUaq or aquaq, the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array AP is overwritten by the upper triangular part of the updated matrix. Before entry, with UPLO = aqLaq or aqlaq, the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero.

Pages related to zspr

  • zspr (3)
  • zsprfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
  • zspcon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
  • zspmv (l) - performs the matrix-vector operation y := alpha*A*x + beta*y,
  • zspsv (l) - computes the solution to a complex system of linear equations A * X = B,
  • zspsvx (l) - uses the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
  • zsptrf (l) - computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
  • zsptri (l) - computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
  • zsptrs (l) - solves a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
  • zscal (l) - ZSCAL scale a vector by a constant